The graph provided shows the function $m(x)$, and the question asks which equation in factored form corresponds to the given graph. Let us analyze the graph to identify its key features:

1. Roots/Zeros: The function crosses the x-axis at $x = -1$, $x = 3$, $x = 5$, and $x = 15$. Therefore, the equation must have these factors:
   $(x + 1)$, $(x - 3)$, $(x - 5)$, and $(x - 15)$.

2. Behavior at Roots: The graph crosses the x-axis cleanly at all roots, suggesting that each root has an odd multiplicity (likely 1). Thus, the factors appear exactly once in the equation.

3. End Behavior: As $x \to -\infty$, $m(x) \to -\infty$, and as $x \to \infty$, $m(x) \to \infty$. This indicates the degree of the polynomial is odd and the leading coefficient is positive.

Answer:

The correct equation that matches the graph is:
$m(x) = (x + 1)(x - 3)(x - 5)(x - 15).$

This corresponds to the fourth option.

Would you like me to verify this further or explain any specific step in more detail? Here are some related questions for deeper understanding:

1. What determines the multiplicity of roots based on the graph's behavior near the x-axis?
2. How does the degree of a polynomial influence its end behavior?
3. Why does the leading coefficient matter for the shape of the graph?
4. How can the factored form of a polynomial be expanded into standard form?
5. Can a polynomial have the same x-intercept appear more than once?

Tip: To identify the correct factored form, always examine the x-intercepts and their behaviors on the graph.